At the terrestrial magnetopause the dense magnetosheath flowing around the magnetosphere interfaces with the normally much more tenuous magnetospheric plasma. Temporal variations in the solar wind dynamic pressure cause the magnetopause to be in continuous motion. When it decelerates and rebounds sunward after a strong and rapid drop in the solar wind dynamic pressure, we have a situation of a heavy-over-light plasma in an effective gravitational field. In this paper we investigate theoretically the conditions under which this configuration may become Rayleigh-Taylor (RT) unstable. The motion of the magnetopause is studied using a gas-dynamic model which takes into account forces arising from hypersonic flow past an object of prescribed shape. Thus the effect of the magnetic field near the magnetopause is not included. For sufficiently large and rapid dynamic pressure variations we obtain accelerations ≥1 km s-2 lasting for periods of the order of 1--2 min. We discuss the possible instability of both global (&lgr;≫Δ, thickness of the magnetopause) and internal (&lgr;<Δ) modes, taking into account the stabilizing effects of (1) magnetic shear across the magnetopause and (2) viscosity of the magnetosheath plasma. We find that both modes are stable when the magnetic shear across the magnetopause is large. When the magnetosheath field points strongly northward, however, we find that both modes may be RT unstable. Among the effects of RT instability on the magnetopause and its environs are (1) large distortions of the magnetic field lines, (2) localized compressions of the magnetospheric magnetic field, (3) increased magnetopause thickness, and (4) reduced average density gradient across the magnetopause. (Since we only concentrate here on the linear stage of the development of the instability, no mass transfer into the magnetosphere is included.) These are all, in principle, observable effects, though the rapid motion of the magnetopause would require a fortuitous spacecraft-magnetopause configuration for them to be actually seen in single-spacecraft data. This work may be considered as a contribution to the current research on the structure and physics of the low-shear magnetopause. ¿ American Geophysical Union 1996